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Polar codes for broadcast channels

Author(s): Goela, N; Abbe, Emmanuel; Gastpar, M

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Abstract: Polar codes are introduced for discrete memoryless broadcast channels. For m-user deterministic broadcast channels, polarization is applied to map uniformly random message bits from m-independent messages to one codeword while satisfying broadcast constraints. The polarization-based codes achieve rates on the boundary of the private-message capacity region. For two-user noisy broadcast channels, polar implementations are presented for two information-theoretic schemes: 1) Cover's superposition codes and 2) Marton's codes. Due to the structure of polarization, constraints on the auxiliary and channel-input distributions are identified to ensure proper alignment of polarization indices in the multiuser setting. The codes achieve rates on the capacity boundary of a few classes of broadcast channels (e.g., binary-input stochastically degraded). The complexity of encoding and decoding is O(n log n), where n is the block length. In addition, polar code sequences obtain a stretched-exponential decay of O(2-nβ) of the average block error probability where 0 < β < 1/2. Reproducible experiments for finite block lengths n = 512, 1024, 2048 corroborate the theory.
Publication Date: 2015
Citation: Goela, N, Abbe, E, Gastpar, M. (2015). Polar codes for broadcast channels. IEEE Transactions on Information Theory, 61 (758 - 782. doi:10.1109/TIT.2014.2378172
DOI: doi:10.1109/TIT.2014.2378172
Pages: 758 - 782
Type of Material: Journal Article
Journal/Proceeding Title: IEEE Transactions on Information Theory
Version: Author's manuscript

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